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    Re: Parallax of Right Ascension and Parallax of Declination
    From: Peter Monta
    Date: 2015 Nov 4, 15:03 -0800

    ​Hmm. Correct me if I am wrong, but my understanding is that the purpose of a world-wide geodetic survey during the 1970s (particularly during the 1970s, but probably started before and certainly continued after) ​was to determine a map showing, for any point on the earth's surface, to what extent a gravitationally determined zenith axis (that is, an axis normal to a horizontal plane determined by a sensitive bubble level) did not pass through the centre of a spherical earth. 

    Yes, geoid models do this---they've been getting better and better.  The new one from NGS based on their GRAV-D effort is said to be good to a few centimeters across North America, and the global ones are almost as good.  Eventually the model will have to start varying with time, similar to the way ITRF needs velocities.

    A geoid was then created which effectively adjusted the latitude and longitude of every point on the surface of the earth such that, to first order, these deviations of local gravity were corrected for. That geoid is WGS84. 

    WGS84 is just the geometrical coordinate system, not including any geoid model.  So WGS84 specifies just the ellipsoid size and shape and center point (the geocenter), and is then realized by a set of control-station coordinates.  The geoid, though, is a gravity equipotential surface, and is a different beast.

    If the latitudes and longitudes according to WGS84 are used for a given place on the earth, you should find that a vertical axis normal to the local gravitationally determined horizontal plane will pass through the centre of the geoid.

    No, this can never happen---there is no coordinate system that can make gravity deflections go away.  WGS84 and friends do the best they can, so that the magnitudes of deflections of the vertical over the ellipsoid are (approximately) minimized globally in a least-squares sense, but they are still as large as they ever were, and they don't pass through the geocenter except maybe in a few magic places.  (I assume by "centre of the geoid" you mean center of mass.)


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